This sounds like the scam. You think you're communicating with someone of age. You have your conversation and some hours or a day later, you get a call from an irate parent who asks you for money. We actually get this question fairly often.
You don't give in to blackmailers. If you do, the money for the phone will only be the first installment, and you'll be paying off these predators for the rest of your life. Blackmail is a crime, and you don't want to allow anyone the power to control your whole life. Do not send any money.
You need to cease all contact with these people and block them so that they can have no further contact with you. As I have said, their "daughter," if she exists at all, is guilty of a crime here, and the evidence that they will have will show that you never asked for pictures, never discussed sexual contact, and you sent her nothing explicit yourself. So they don't have a lot of incentive to report this if it's true. They are only trying to extort money from you and when they won't be able to manipulate you, they will likely move on to someone else they can intimidate. In all the time we have seen this "Sextortion scam" we have never been informed by even one customer that the threat was carried out.
To feel more safe, however, you can go talk to a local criminal lawyer. Let him or her see the correspondence, because if it's favorable to your position, you can be proactive and report THEM to the police for fraud and extortion.